What is the probability that the human chess champion wins a majority of the game? Equation to deal with the problem?

Question

the maker of a computer chess game claims the game can beat a human chess champion 35& of the time. A human chess champion plays ten games against the computer. Assuming the manufactures claim is true, you are interested in the probability that the human chess champion wins a majority of the games. 

Answer 1

Assuming the manufactures claim is true -- Corrected: Assuming the manufacturer's claim is true...

 

This is Binomial Distribution probability; p, the probability of success, is 0.65--success being a win for the human.

q=0.35; n=10.

P(human wins 6 or more times) is 10C6•p⁶•q⁴ + 10C7•p⁷•q³ + 10C8•p⁸•q² + 10C9•p⁹•q +10C10•p

I will let you calculate this!

 

There are ways to evaluate this on a Graphing Calculator--binomial probability functions available under DISTR menu, on TI-84, for example.